This is wonderful. As part of a cryptography course in undergrad, I spent a fair number of hours adding/multiplying points on small curves by hand and eventually computationally, and seeing these animations represents the "feel" of that process better than any resource I have seen.
It seems that elliptic curves are used quite shrewdly in public key exchanges, used as a sort of off-the-shelf arithmetic system that renders some benefits (harder to solve the elliptic curve discrete log problem) and drawbacks (more expensive to compute, because of these point ops) compared to key exchanges relying on the integer discrete log problem. There is generally much energy spent on explaining the point operations but not much on explaining this context: this is an alternate arithmetic inserted into the Diffie Helman scheme that is secure and not so hard to work with.
The finite fields in application (e.g. in X25519) are so large compared to the toy examples that the technical details matter more for understanding the performance of the algorithms than the actual cryptographic method. Understanding (and convincing yourself of) the core behavior of the key exchange itself is perhaps best done with the number theory and group theory lens. There was a discussion here on HN a couple days ago which largely bashed the theoretical approach in favor of simply cargo culting the tools, which was appalling. I hope they all enjoy this link!
Anyhow, the application of elliptic curves to cryptography is clever and I would recommend everyone with an interest (and a little background in algebra) read Koblitz's paper[1] and Miller's earlier description [2] if they are looking for more context for OP's wonderful presentation.
It seems that elliptic curves are used quite shrewdly in public key exchanges, used as a sort of off-the-shelf arithmetic system that renders some benefits (harder to solve the elliptic curve discrete log problem) and drawbacks (more expensive to compute, because of these point ops) compared to key exchanges relying on the integer discrete log problem. There is generally much energy spent on explaining the point operations but not much on explaining this context: this is an alternate arithmetic inserted into the Diffie Helman scheme that is secure and not so hard to work with.
The finite fields in application (e.g. in X25519) are so large compared to the toy examples that the technical details matter more for understanding the performance of the algorithms than the actual cryptographic method. Understanding (and convincing yourself of) the core behavior of the key exchange itself is perhaps best done with the number theory and group theory lens. There was a discussion here on HN a couple days ago which largely bashed the theoretical approach in favor of simply cargo culting the tools, which was appalling. I hope they all enjoy this link!
Anyhow, the application of elliptic curves to cryptography is clever and I would recommend everyone with an interest (and a little background in algebra) read Koblitz's paper[1] and Miller's earlier description [2] if they are looking for more context for OP's wonderful presentation.
1: Koblitz: Elliptic Curve Cryptosystems https://www.ams.org/journals/mcom/1987-48-177/S0025-5718-198...
2: Miller: Use of Elliptic Curves in Cryptography https://link.springer.com/chapter/10.1007/3-540-39799-X_31